Nature © Macmillan Publishers Ltd 1998 8 letters to nature NATURE | VOL 396 | 26 NOVEMBER 1998 | www.nature.com 35360% of the electrons are actually injected into state 3. If we assume that the remaining 40% is then in level 4, and that a w~l 2 , a dependence characteristic of free-carrier absorption, we obtain a theoretical estimate for J 41 th of 3.8 kA cm -2 . The discrepancy with the experimental value probably originates from electrons in higher states of the upper miniband (see also the data of Fig. 4) and from direct scattering from the injector to the lower miniband, which leads to non-unity injection ef®ciency into 3 and 4. At high bias, the doping charges in the injector are no longer suf®cient to keep the superlattices free of electric ®eld. Therefore, the superlattice translation and re¯ection symmetries are spoiled and transitions which are suppressed in an ideal superlattice can acquire large dipole matrix elements. In particular, 4±2 (which is diagonal in k-space) is the one responsible for the l 7:3 mm laser emission.More information on the actual behaviour of our structure can be obtained by analysing the luminescence spectra (Fig. 4). Three peaks with a width of ,15 meV are clearly identi®ed, in correspondence with the energy of each of the lasing transitions. Although the relative intensity of the peaks depends on the wavelength response of the experimental set-up, it is evident from Fig. 4 inset that the intensity of the 4±2 peak increases with current density more rapidly than that of the other peaks, which we expect in view of its oscillator strength increasing (and the other two decreasing) with bias. Emission at larger energies (>220 meV) is also detected, due to transitions from states higher in the miniband.We note that a complete localization of the states over one or two wells induced by the penetration of the electric ®eld 24 would give rise to completely different spectra, and is not compatible with the smooth and monotonic current±voltage curves we observe. Furthermore, the density of carriers stored in the upper miniband at threshold is estimated from the lifetimes to be ,6 3 10 10 cm 2 2 , far less than the sheet density of doping in the injectors, which ensures negligible space-charge electric ®elds caused by the injection. To estimate the threshold for lasing on the 4±2 transition, we cannot use equation (1), because the population n 4 in level 4 is, to a ®rst approximation, locked to its value at the threshold for the 4±1 transition. The threshold for 4±2 lasing is instead reached by a different mechanism (laser action by oscillator strength tuning 17 ). As the penetration of the electric ®eld into the superlattice increases, the dipole matrix element z 42 is enhanced until the gain equals the optical losses (laser threshold condition). Roughly speaking then, J 42 th should be determined by the condition that the applied voltage is such that z 42 < z 41 , which occurs at 7.3±7.4 V, in fair agreement with the measured 7.7 V.M Figure 3 Comparison of the ®rst-order kinetic rate co...

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A novel united atom force field affords accurate and quantitative reproduction of the adsorption properties of linear and branched alkanes in nanoporous framework structures. The force field was generated by adjusting the parameters so as to faithfully reproduce the experimentally determined isotherms (particularly the inflection points) on MFI-type zeolite over a wide range of pressures and temperatures. It reproduces extremely well the Henry coefficients, heats of adsorption, preexponential factors, entropies of adsorption, and maximum loading. It is shown that the extension of the force field from MFI to other nanoporous framework topologies is successful, that it affords the prediction of topology-specific adsorption properties, and that it can be an effective tool to resolve the many discrepancies among experimental data sets.

Shape selectivity is a simple concept: the transformation of reactants into products depends on how the processed molecules fit the active site of the catalyst. Nature makes abundant use of this concept, in that enzymes usually process only very few molecules, which fit their active sites. Industry has also exploited shape selectivity in zeolite catalysis for almost 50 years, yet our mechanistic understanding remains rather limited. Here we review shape selectivity in zeolite catalysis, and argue that a simple thermodynamic analysis of the molecules adsorbed inside the zeolite pores can explain which products form and guide the identification of zeolite structures that are particularly suitable for desired catalytic applications.Z eolites are microporous mineral materials that have found wide use in industry since the late 1950s, with one of their most important applications being chemical catalysis. They are particularly important as cracking catalysts in oil refining. One of their defining features-apart from being solid catalysts that are easy to recycle-is that the shape, or topology, of the internal pore structure of a zeolite can strongly affect the selectivity with which particular product molecules are formed in chemical transformations catalysed by the zeolite. Here, we will argue that this shape selectivity can be explained by very simple thermodynamic analyses that consider the impact of zeolite topology on the free energy landscape; that is, on the free energies of formation of the various molecules involved in the catalysed reactions.The analyses presented here are simple and straightforward, yet have become feasible only relatively recently as advances in molecular simulation techniques have started to provide access to the thermodynamic data underpinning them. After a short introduction of zeolites and their use as catalysts, we will therefore also briefly outline the developments in simulation capabilities that give access to the thermodynamic information crucial for our understanding of zeolite catalysis. We then show how the free-energy-landscape approach can elucidate the molecular-level mechanism(s), giving rise to shape selectivity in a number of simple yet industrially important processes. We conclude this review by outlining the crucial issues that need to be addressed to take the free-energy-landscape approach to the next stage, where the combined use of simulations and thermodynamic analysis might have profound implications for how we screen and develop zeolite-based catalysts. Zeolites as industrial catalystsZeolites are crystalline aluminosilicates with a three-dimensional framework that consists of nanometre-sized channels and cages and imparts high porosity and a large surface area to the material. The basic structural unit of all zeolite frameworks consists of a silicon or aluminium atom tetrahedrally coordinated to four oxygen atoms. Any zeolite built of silica and oxygen only is neutral, but replacing Si 41 by Al 31 creates a negative charge on the framework. All such framework ch...

Abstract:We have developed a united atom force field able to accurately describe the adsorption properties of linear alkanes in the sodium form of FAU-type zeolites. This force field successfully reproduces experimental adsorption properties of n-alkanes over a wide range of sodium cation densities, temperatures, and pressures. The force field reproduces the sodium positions in dehydrated FAU-type zeolites known from crystallography, and it predicts how the sodium cations redistribute when n-alkanes adsorb. The cations in the sodalite cages are significantly more sensitive to the n-alkane loading than those in the supercages. We provide a simple expression that adequately describes the n-alkane Henry coefficient and adsorption enthalpy as a function of sodium density and temperature at low coverage. This expression affords an adequate substitute for complex configurational-bias Monte Carlo simulations. The applicability of the force field is by no means limited to low pressure and pure adsorbates, for it also successfully reproduces the adsorption from binary mixtures at high pressure.

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We present a method to determine potential parameters in molecular simulations of confined systems through fitting on experimental isotherms with inflection points. The procedure uniquely determines the adsorbent-adsorbate interaction parameters and is very sensitive to the size parameter. The inflection points in the isotherms are often related to a subtle interplay between different adsorption sites. If a force field can predict this interplay, it also reproduces the remaining part of the isotherm correctly, i.e., the Henry coefficients and saturation loadings. DOI: 10.1103/PhysRevLett.93.088302 PACS numbers: 82.75.Jn, 47.55.Mh, 66.30.-h The effect of confinement on adsorption and diffusion is still poorly understood despite its importance for practical applications. The performance of molecular sieves in separation and catalytic processes depends critically on the match between sieve topology and the shape and size of the adsorbate [1]. It is therefore of considerable industrial importance to explore the adsorption and diffusion of linear and branched alkanes in different topologies using realistic simulations at the microscopic level [2]. Different parameter sets yield values of diffusivities that differ not only quantitatively but also show a different qualitative dependence on the molecular loading [3]. The critical unresolved question follows: Which of these parameter sets is the most physically realistic one? Here, we hope to remedy this situation.Potential parameter sets can be checked only via comparison with experiment. For diffusion the comparison is complicated by large discrepancies between microscopic and macroscopic experimental measurement methods, and even within the same measurement technique there are many disagreements between various studies. However, adsorption results seem to be well established and provide a more solid basis for a detailed comparison between experiment and simulation. Moreover, a large amount of data exists on adsorption of hydrocarbons in siliceous zeolites.Silicalite-1 (Fig. 1) consists of a three-dimensional pore system with straight parallel channels, intersected by zigzag channels [4]. The channels of approximately 6 Å in diameter lead to shape selectivity, especially for the isomers of hexane, which have dimensions close to the silicalite-1 pores. The linear channels intersect with the zigzag channels 4 times per unit cell. Interestingly, for n-heptane and for the branched alkanes in silicalite-1 a kink in the isotherm is observed [5]. This inflection is directly related to the number of intersections in the structure and occurs at exactly four molecules per unit cell. As these inflections are caused by a subtle interplay between the size and configuration of the molecule and two different adsorption sites, it becomes clear that the adsorbent-adsorbate potential size parameter is the most sensitive parameter in the force field.In general, adsorption in any periodic structure has steps or kinks. The reason is that steps and kinks signal transitions between diffe...

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